摘要
本文采用波函数展开方法提出弹性半空间表面一任意圆弧形凸起边界对平面ＳＨ波二维散射的封闭级数解答．利用引入的辅助函数和推广的外域型Ｇｒａｆ加法公式将解答归结为一组无穷代数方程组的求解．解答的数值结果可由无穷方程的截断计算得出。文中从级数项数增加时计算结果的收敛以及边界条件的收敛满足两方面检验了截断计算的精度，并指出了位移解答的收敛速度与主要参数之间的关系．同时，对凸起角点的应力奇异性及其对解答精度的影响进行了说明．最后，给出了一些算例说明凸起地形高宽比对地面运动的影响，并提供了两组典型算例及其数值结果供各种近似方法对比。
A closed- form solution of two-dimensional scattering of plane SH waves by a cylindrical hill of circular-arc cross-section in a half-space is presented using the wave functions expansion. The solution is reduced to solving a set of infinite linear algebraic equations using the auxiliary functions and the exterior region form of Graf's addition theorem. Numerical solutions are obtained by truncation of the infinite equations and the accuracy is demonstrated by convergence of the numerical results and by the extent to which the numerical results fit the exact boundary conditions with the increasing of the truncation order. The singularity in the shear stress near the rim of the hill is evaluated and its effect on the accuracy of the numerical results is explained.The figures and their data for the numerical results of two typical cases are then given for comparison with various approximate methods and the effects of the height-to-width ratio of the hill on surface ground motion are finally illustrated.
出处
《地震工程与工程振动》
CSCD
北大核心
1996年第2期1-13,共13页
Earthquake Engineering and Engineering Dynamics
基金
国家自然科学基金
地震科学联合基金
关键词
地面运动
凸起地形
封闭解
SH波
hill,scattering, closed-form solution, ground motion
